Discounts

A discount is a deliberate reduction in price from an item's Marked Price (or List Price), typically expressed as a percentage. For example, a 20% discount on a $100 item results in a $20 Discount Amount and an $80 final Selling Price. This strategy is crucial for businesses, serving multiple purposes: it encourages immediate sales, helps clear out old inventory, promotes new services, and acts as a powerful marketing tool to attract new customers and boost retention. Discounts have played an important role in commerce for centuries, evolving from ancient bartering and loyalty-based pricing to the structured seasonal sales and coupons popularized by department stores and companies such as Coca-Cola in the late nineteenth century. They are now foundational to both physical retail and global e-commerce.

The Discount Formula plays a significant role in how to calculate discount. The Discount Amount is calculated using the core relationship between the initial price and the final price paid:
 

\(\text{Discount Amount} = \text{List Price} - \text{Selling Price}\)
 

Understanding the difference between the Cost Price (what the business paid), the List Price (the advertised price), and the Selling Price (the final price paid by the customer) is crucial. The Discount Percentage (or Discount Rate) is the reduction expressed relative to the List Price. The Rate Formula for finding this is:
 

\(\text{Discount Percentage} = \frac{\text{Discount Amount}}{\text{List Price}} \times 100\)
 

Discounts enable customers to purchase desired items without significantly affecting their budget. For sellers, they enable quick stock turnover and market penetration, cementing discounts' role as a vital component of modern marketing and trade.
 

Discounts have several properties that show how they work in math and in businesses.

• The original price will always get reduced. Regardless of the discount percentage, the selling price will always be less than the list price.

• When multiple discounts are given, they are applied one after the other. They are not added together. So, if a product has a 20% discount, first and then another 10% discount. The second discount is applied to the new reduced price and not the list price.

• Discounts can be a fixed amount or a percentage of the original price.

Discounts are usually offered when purchasing an item from a seller or manufacturers. There are three types of discounts:

Trade Discounts

This discount is usually offered by the distributor to the seller, not the end customer. Distributors usually have items in huge quantities and offers the item to the retailer for a reduced price.

Quantity Discounts

If a customer buys products in huge quantities from the seller, then quantity discounts would be offered to the customer. This is usually offered to attract customers to buy large quantities of an item.

Promotional Discounts

Most stores or manufacturers offer promotional discounts when a new product is in stock or when there is a clearance sale. Some sellers also promote a “buy one, get one free” offer.

There are a few formulas we use to calculate discounts:

• Discount = List Price - Selling Price

•  Discount % = \(\left(\frac{\text{Discount}}{\text{List Price}}\right) \) × 100

• Discount = \(\frac{\text{Discount} \%}{100} \) × List price

• Selling Price = List Price - Discount

Understanding the concept of discounts can be quite easy. But it can get quite confusing, so here are a few easier approaches to make it much easier. Here are some tips and tricks:

• Memorize the basic discount formula: Students must memorize the basic discount formulas. Practice with real-life problems and different values to get comfortable with the formulas.

• Learn to quickly calculate percentages: Try to learn ways to calculate percentages of a number. For example, to find 10% of a number we need to move the decimal point one place to the left. So, 10% of 500 is 50.

• Practice in the real world: When you go shopping the next time, you can check the discount tags and calculate the final price yourself. You could even compare different discounts and find out what would be a better deal.
   
• Break big discounts into smaller steps: Instead of calculating a tricky percentage at once, break it into parts. For example, to find 25% of 400, first find 10% (40), then double it (80 = 20%), and add half of 40 (20 = 5%). So, 25% = 100.
   
• Compare successive discounts with a single discount: Sometimes shops give two discounts (like 20% + 10%). Remember, these are not the same as a flat 30%. Use the formula: Final Price = Marked Price × (1 – first discount) × (1 – second discount).

Discounts are applied in all kinds of shops, groceries, or online stores. Here are a few other real-world applications where we apply discounts.
 

• Many companies such as Amazon and Apple Music offer discounts that are specifically for students. These are discounts targeted only towards students.
   
• Many Fast food restaurants and cafés offer seasonal discounts to gather more customers and promote their seasonal items.
   
• Gyms offer discounts on memberships for customers based on the gym’s packages.
   
• Travel and Transportation Discounts: Airlines, railways, and bus services often provide discounts for early bookings, group travel, or for senior citizens and students.
   
• Festival and Holiday Sales: During occasions like Black Friday, Diwali, or Christmas, retail stores and e-commerce platforms give massive discounts to boost sales.